Revealed Preference Theory, Ordering and the Axiom of Sequential Path Independence

Abstract

This paper is concerned with the axiomatic foundation of the theory of choice. Describing a choice procedure which one often observes in real life, this paper shows that the requirement of path independence of such a procedure is a necessary and sufficient condition for transitive or full rationalization of a choice function, i.e. the existence of a preference ordering. It is shown that our result holds when rationality is identified with different interpretations of the binary relations of preference revealed by a choice function, e.g. the revealed preference relation of Arrow, the wide revealed preference relation of Richter. It is also shown that a weaker version of our path independence condition is both necessary and sufficient for a rational choice.

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